Related papers: Standard dilations of q-commuting tuples
We give an $n$-space generalized $q$-binomial theorem, and some new $q$ series identities that resemble the traditional $q$ series partition generating functions. These identities enumerate stepping stone weighted vector partitions.
We investigate the prescribed Q-curvature flow for GJMS operators with non-trivial kernel on compact manifolds of even dimension. When the total Q-curvature is negative, we identify a conformally invariant condition on the nodal domains of…
We consider the restricted subsets of $\mathbb{N}_n=\{1,2,\ldots,n\}$ with $q\geq1$ being the largest member of the set $\mathcal{Q}$ of disallowed differences between subset elements. We obtain new results on various classes of problem…
Fock space constructions give rise to natural exchangeable families and are thus well suited for cumulant calculations. In this paper we develop some general formulas and compute cumulants for generalized Toeplitz operators, notably for…
We consider deformations of CFTs from the perspective of parallel transport in moduli space. In particular, we show how the deformations of individual operators can be computed and we also explore how these ideas can be extended to more…
We introduce a noncommutative analogue of the absolute value of a regular operator acting on a noncommutative $\mathrm{L}^p$-space. We equally prove that two classical operator norms, the regular norm and the decomposable norm are…
In this proceedings a particular example from \cite{KMPY} (q-alg/9603025) is presented: the construction of the level 2 Fock space of $\U_q(\affsl{2})$. The generating ideal of the wedge relations is given and the wedge space defined.…
We introduce a $q$-deformation of the Fock space of holomorphic functions on $\mathbb{C}$, based on a geometric definition of $q$-analyticity. This definition is inspired by a standard construction in complex differential geometry. Within…
In this paper we give a sharp estimate on the norm of the scaling operator $U_{\lambda}f(x)=f(\lambda x)$ acting on the weighted modulation spaces $\M{p,q}{s,t}(\R^{d})$. In particular, we recover and extend recent results by Sugimoto and…
The general affine group $G_n$ sits at the intersection of harmonic analysis on solvable groups and the geometry of negatively curved symmetric spaces. In this work, we characterize the $L^p$-behavior of maximal operators associated with…
Quantum supermaps are higher-order maps transforming quantum operations into quantum operations. Here we extend the theory of quantum supermaps, originally formulated in the finite dimensional setting, to the case of higher-order maps…
We show that for all q in the interval (-1,1), the Fock representation of the q-commutation relations can be unitarily embedded into the Fock representation of the extended Cuntz algebra. In particular, this implies that the C*-algebra…
Let $Q_n=[0,1]^n$ be the unit cube in ${\mathbb R}^n$ and let $C(Q_n)$ be a space of continuous functions $f:Q_n\to{\mathbb R}$ with the norm $\|f\|_{C(Q_n)}:=\max_{x\in Q_n}|f(x)|.$ By $\Pi_1\left({\mathbb R}^n\right)$ denote a set of…
The main result of this paper is that there is sometimes a triangulated equivalence between $D_Q( A )$, the $Q$-shaped derived category of an algebra $A$, and $D( B )$, the classic derived category of a different algebra $B$. By…
We describe the $C_2$-equivariant homotopy type of the space of commuting n-tuples in the stable unitary group in terms of Real K-theory. The result is used to give a complete calculation of the homotopy groups of the space of commuting…
The q-deformed Fock spaces of higher levels were introduced by Jimbo-Misra-Miwa-Okado. The q-decomposition matrix is a transition matrix from the standard basis to the canonical basis defined by Uglov in the q-deformed Fock space. In this…
We prove an estimate for Donaldson's $Q$-operator on a prequantized compact symplectic manifold. This estimate is an ingredient in the recent result of Keller and Lejmi about a symplectic generalization of Donaldson's lower bound for the…
In this paper a systematic study of unitary asymptotes of commuting $n$-tuples of general Hilbert space operators is initiated. Special emphasis is put on the study of the quasianalicity property.
This investigation pertains to the construction of a class of generalised deformed derivative operators which furnish the familiar finite difference and the q-derivatives as special cases. The procedure involves the introduction of a linear…
We discuss the problem posed by Bender, Coley, Robbins and Rumsey of enumerating the number of subspaces which have a given profile with respect to a linear operator over the finite field $\mathbb{F}_q$. We solve this problem in the case…